Amazon has just launched a new video streaming iPad application - Amazon Instant Video - in the App Store. Not only does the new, free app allow users to stream thousands of Prime Instant Videos to their iDevice, but users of the application also have the option of saving purchased and rented videos to their iPad for offline viewing.
As outlined in the app's release notes:

Watch thousands of titles available from Prime Instant Video at no additional cost with an Amazon Prime membership and over 120,000 videos available from the Amazon Instant Video store by installing the Amazon Instant Video app. Download purchased and rented videos from Your Video Library for offline viewing on airplanes, road trips, or any time a WiFi connection is unavailable. Keep track of movies and TV shows to watch later by adding them to Your Watchlist. A selection of top Prime Instant Video titles is included in the app, and you can visit Amazon to add other Prime titles to Your Watchlist. Start watching a video on an iPad and Whispersync technology automatically syncs your place between devices, allowing videos to be resumed from where you left off on a Kindle Fire, PS3, PC, Mac, or hundreds of models of connected TVs and Blu-ray players.

Features of Amazon Instant Prime include:

Stream thousands of titles available from Prime Instant Video at no additional cost with a Prime membership, or watch over 120,000 videos available from the Amazon Instant Video store

Download purchased and rented videos from Your Video Library

Shop over 120,000 videos available from the Amazon Instant Video store by visiting Amazon

Add videos to your Watchlist from a PC, Mac, or Kindle Fire for later viewing on your iPad

Subscribe to a TV Season Pass by visiting Amazon and episodes will automatically be available on your iPad the day after they air

Start watching on your iPad, and resume watching right where you left off on a Kindle Fire, PS3, PC, Mac, or hundreds of models of connected TVs and Blu-ray players with Amazon Whispersync.

Just yesterday, a brand-new Hulu Plus channel started appearing on Apple TVs. Now, Prime members can also get their on-demand video fix on an iDevice (well, an iPad - no iPhone version has yet launched) for no extra cost. The downside of this new app is, as 9to5Mac notes, that AirPlay streaming appears to be working with just audio, and not video. But it's possible that Amazon will correct this in a future update, so don't condemn the app yet.
Either way, it's a nice App Store addition and will certainly be appreciated by preexisting Prime subscribers. For more information, take Amazon Instant Video for a spin yourself. As mentioned, it's available in the App Store for free.